Abstract

We consider admissible encodings on an elliptic curve, that is, the hash functions that map bitstrings to points of the curve. We extend the framework of admissible encodings, known from CRYPTO 2010 paper, to some class of non-deterministic mapping algorithms. Using Siguna Müller’s probabilistic square root algorithm we show a mapping that works efficiently for any finite field \(\mathbb{F}_q\) of characteristic greater than 3, and that is immune to timing attacks. Thereby we remove limitations of the mappings analyzed in the CRYPTO 2010 paper. Consequently, we remove limitations of a so called PACE Integrated Mapping protocol, which has recently been standardized by ICAO, and is used to protect contactless identity documents against unauthorized access.

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The paper has been supported by the Polish Ministry of Science and Higher Education: during the initial stage (i.e., numerical experiments) by project O R00 0015 07, later by project N N206 369 839; the third author is supported by the Foundation for Polish Science, “Mistrz” Programme.